Combine the rice vinegar and 2 tsp. salt in a large bowl. Let sit to dissolve the salt. Put the potatoes and 2 Tbs. salt in a 6-quart pot and add enough cold water to cover by 1 inch. Bring to a boil over high heat and reduce the heat to maintain a simmer. Cook the potatoes until barely tender when poked with a fork or skewer, 20 to 25 minutes. If the potatoes aren't all the same size, remove them as they are cooked. (Baby potatoes will take 5 to 10 minutes.)

Gently drain the potatoes in a colander and set aside until just cool enough to handle. Using a paring knife, peel the potatoes by scraping off the skin. (Skip this step if using baby potatoes.) Cut the potatoes into 3/4-inch chunks. Add the potatoes to the bowl with the vinegar and gently stir with a spatula to coat. With your fingers, pull apart any pieces that are stuck together.

When the potatoes have completely cooled, gently fold the red onions, celery, bacon, hard-boiled eggs, and parsley into the potatoes. Fold in enough dressing to generously coat the potatoes (you may not need all of the dressing). Season to taste with salt and pepper. Serve at room temperature or cold.